In general, a machine for processing a magnetic resonance image acquires a tomographic image of a specific body part of a patient by using a resonance phenomenon resulting from supply of electromagnetic energy. This machine for processing a magnetic resonance image is being widely used since it does not result in radiation exposure and can relatively easily acquire a tomographic image, compared to imaging machines such as X-ray and CT.
To briefly describe a method for producing a magnetic resonance image, a high frequency RF signal is applied to a target for magnetic resonance imaging a multiple number of times so as to excitate spin of atomic nucleuses within the target. Through application of a pulse train to the magnetic resonance machine, the magnetic resonance image processing machine generates various signals such as a free induction decay (FID) signal and spin echo, and selectively acquires the signals to produce a magnetic resonance image.
Although the magnetic resonance image processing machine has had a limit in that it requires long imaging time, compared to other imaging equipment, a compressed sensing technique has been introduced as a method for reducing the imaging time. The compressed sensing technique demonstrated that when an original signal has sparsity, the original signal can be reconstructed, even though a sample frequency is lower than the Nyquist sampling frequency. In this case, in order to reconstruct the original signal through the compressed sensing technique, it is necessary to transform the original signal to a domain where the sparsity of the original signal is maximized, and the original signal is reconstructed through a method that repeatedly estimates the original signal to maximize the sparsity of the original signal in the transform domain.
To more specifically describe the compressed sensing technique, since MRI collects an image signal in a k-space, the compressed sensing is also accomplished in the k-space. With respect to a method for scanning the k-space, there is rectilinear or spiral scanning or others. In order to reconstruct an image through the compressed sensing technique, the following three (3) requirements should be met: first, an original image should have sparsity in a specific transform domain; second, an aliasing artifact should be incoherent when a sampling frequency is lower than the Nyquist sampling frequency in the k-space; and third, a repeated image reconstruction method that maximizes the sparsity of the original image signal and consistency between a measured image signal and an estimated image signal is necessary.
This conventional compressed sensing imaging method implements variable density random under sampling that acquires data with high density in the center of the k-space, i.e., a low frequency domain, and data with low density in the periphery of the k-space, i.e., a high frequency domain. Through this sampling method, an inconsistent aliasing signal appearing in an image can be removed together with noise in a sparse space.
Meanwhile, in this regard, a prior article (Lusting et al., Sparse MRI: The application of compressed sensing for rapid MR imaging, Magn. Reson. Med., vol. 58, pp. 1182-1195, 2007) describes a compressed sensing technique that implements signal restoration by transforming a whole image to one sparse space.